Looking over the last several posts, I see absolutely nothing related to space flight applications. All I see is more of exactly what got the previous version of this thread to disappear for a while.

I would respectfully disagree. I find the discussion both highly pertinent to possible space flight applications and quite thought provoking. We must not lose the forest for the trees, but at the same time, it is difficult to comprehend the forest without the trees.

None of these experiments have demonstrated a linear acceleration: all of them have measured rotational accelerations. None of the EM Drives have been tested in a vacuum. None of the measured forces are high enough to levitate the drive.

Forget about levitation. I havent read much or anything about it, but are the forces even in the same ballpark as existing magnetic torquer rods for cubesats ? If yes, in theory this could assist with attitude control in deep space, at least for desaturation.

Anyone ? Anyone ?

I mean, actual spaceflight application. Desaturation spends fuel. Can we get a propellantless desaturation device, with main attitude control provided by reaction wheels ?

Again, from the claimed experimental setups, are the reported angular momentums even on a scale where they could turn a cubesat - even if it takes a long time to do so ? Its not like torquer rods are fast or anything, but they only work within earths magnetic field.

And if it cannot turn a cubesat, the entire thing is no better than Steorn Orbo, is it ?

A spring (with finite stiffness) attached to a wall NEVER prevents an object attached to it from accelerating, thus Shawyer's statement is not well stated or it is incorrect. Only an infinitely stiff (rigid) spring would prevent an object from accelerating. Otherwise (for finite spring constant) the system will just obey a solution of the second order differential equation: m d^2x/dt^2 +c dx/dt + k x = F.

If the displacement is a function of time, such that the second order derivative of the displacement with respect to time is not zero, there is an acceleration a = d^2x/dt^2 =( F - c dx/dt - k x )/m . In words: the acceleration equals the applied force minus the viscous force, minus the spring force, all divided by the mass.

If the displacement is not a function of time, we have simply (the "steady-state" solution) F=k*x (force=springConstant*displacement)

In the NASA Eagleworks tests of the truncated cone:

1) The truncated cone EM thruster was restrained by the torsional spring constant of the torsional pendulum used for measurement. The torsional spring constant effectively acts like a spring attached to a wall (the difference being that in the NASA Eagleworks test we have a torsional pendulum where the EM Drive performs a rotation instead of a rectilinear motion)

2) The truncated cone EM thruster was initially at rest (prior to power input).

3) A time-varying displacement (effectively due to a rotation around the torsional axis) was recorded and thus a force was calculated by NASA Eagleworks using the known constants of the system.

4) We have verified this: we modeled NASA Eagleworks torsional pendulum, and furthermore analyzed the data using Fourier Transforms to obtain the Power Spectral Density and the Autocorrelation of the response.

Thus:

Shawyer's statement "That a horizontal EM thruster restrained from accelerating horizontally (through an opposing spring) will record no thrust" in http://www.emdrive.com/EmDriveForceMeasurement.pdf is not well stated or it is incorrect, as shown, for example, by the experiments carried out at NASA Eagleworks.

None of these experiments have demonstrated a linear acceleration: all of them have measured rotational accelerations. None of the EM Drives have been tested in a vacuum. None of the measured forces are high enough to levitate the drive.

Forget about levitation. I havent read much or anything about it, but are the forces even in the same ballpark as existing magnetic torquer rods for cubesats ? If yes, in theory this could assist with attitude control in deep space, at least for desaturation.

Anyone ? Anyone ?

I mean, actual spaceflight application. Desaturation spends fuel. Can we get a propellantless desaturation device, with main attitude control provided by reaction wheels ?

...

As an example you can use for calculations, Shawyer reported (for his "Shawyer Demo") a measured force = 0.1023 Newtons (1/10th of a Newton) for a power input of 421 watts.

I thought I would make up a summary of the dispersion relation approach, as I keep doing this in bits and pieces.....

Thanks for the summary, much appreciated.

Quote from: Notsosureofit

The difference from other calculations is that there is a term dependent on the particular mode of the cavity, (X[subm,n])^2, not just the area of the end plates.

Indeed! It is very impressive that not only your calculations are not that far from actual results but that your theory correctly predicts mode dependence and that the magnitude of the mode dependence corresponds with experimental results: the Transverse Electric TE012 mode produces much more [thrust force/input power] than the Transverse Magnetic TM211 mode , which was confirmed by the NASA Eagleworks experiments! Neither the Shawyer nor the simplified McCulloch equations show this mode-dependence.

@Notsosureofit: did you mean to use the "reduced Planck constant", also called "Dirac constant" hbar as in the Latex equations above or did you mean to use the Planck constant h as per your post ?

where

h = hbar * 2 * Pi

Given the de Broglie wavelength λ of a photon and the speed of light c, the energy E of the photon is

E = h c / λ = hbar * 2 * Pi * c / λ

It seems to me that you meant

1) to use h (instead of hbar in the Latex equation)

2) the factors of (Pi^2) in the first Latex equation and 4 Pi^2 in the 2nd Latex equation are in an incorrect position: the factors should be (h/(4 Pi^2)) in the first equation and (1/(c 4 Pi^2)) in the second equation

Thrust per photon, with Planck's constant instead of the reduced constant:

I think that the factors of (Pi^2) in the first Latex equation and 4 Pi^2 in the 2nd Latex equation are in an incorrect position (they should be in the denominator instead of the numerator): the factors should be (h/(4 Pi^2)) in the first equation and (1/(c 4 Pi^2)) in the second equation.

I think that the factors of (Pi^2) in the first Latex equation and 4 Pi^2 in the 2nd Latex equation are in an incorrect position (they should be in the denominator instead of the numerator): the factors should be (h/(4 Pi^2)) in the first equation and (1/(c 4 Pi^2)) in the second equation.

I think that the factors of (Pi^2) in the first Latex equation and 4 Pi^2 in the 2nd Latex equation are in an incorrect position (they should be in the denominator instead of the numerator): the factors should be (h/(4 Pi^2)) in the first equation and (1/(c 4 Pi^2)) in the second equation.

Hmm. Are you sure? Oh well, here they are just the same:

Yes, thanks. That's what I think. But these are @Notsosureofit equations, hopefully he can double check them and see whether he agrees

PS: I agree with Notsosureofit, the second equation would better read NT, where "N" stands for the thrust of all the photons, instead of the thrust of a single photon "T".

Guys, Guys......I stopped reading some time ago.....now we are into the 2nd thread.

Time to "let it go"........prove it one way or another. The energy spent back and forth could have been put into a cad file, exported into STEP or IGES format by now....(someone please do it)

Then maybe if time permits i'll print out a test model.

Someone then talk maybe to Nanoracks, and lets get it tested.

What are STEP and IGES ?

They are graphics file data formats for supposedly "vendor neutral" purposes for digital exchange of CAD (Computer Aided Design) drawings. (As opposed to, for example vendor-specific AutoCad data files, for which you need vendor-provided software like AutoCad to be able to read them).

Imagine if somebody told airplane or rocket developers [if NASA Eagleworks or Shawyer can be compared [?] to the Wright Brothers or Goddard] :"I stopped reading some time ago, it has now been [months (?) for us] since you guys have been writing about this in this forum. Time to "let it go": give me detailed engineering-quality drawings showing how to make this so that I can fabricate it to test whether this flying machine or rocket does indeed fly"

"A self-accelerating electronic wave packet can acquire a phase akin to the Aharonov–Bohm effect, but in the absence of a magnetic field.""The vector potential in question is a gauge-dependent quantity, namely a mathematical construct whose form is not uniquely defined."

"The Aharonov–Bohm effect predicts that two parts of the electron wavefunction can accumulate a phase difference even when they are confined to a region in space with zero electromagnetic field. Here we show that engineering the wavefunction of electrons, as accelerating shape-invariant solutions of the potential-free Dirac equation, fundamentally acts as a force and the electrons accumulate an Aharonov–Bohm-type phase—which is equivalent to a change in the proper time and is related to the twin-paradox gedanken experiment. This implies that fundamental relativistic effects such as length contraction and time dilation can be engineered by properly tailoring the initial conditions. As an example, we suggest the possibility of extending the lifetime of decaying particles, such as an unstable hydrogen isotope, or altering other decay processes. We find these shape-preserving Dirac wavefunctions to be part of a family of accelerating quantum particles, which includes massive/massless fermions/bosons of any spin."

what is the correct force expression for the force on the solenoid andsecond, the assumption that Newton’s third law holds in the sense that thechange of the solenoid’s momentum is compensated by the change of theelectron’s momentum. The discussion of “Feynman’s paradox” shows thatthe latter is not always the case. It is possible that a change in field momentumis an essential part of the Aharonov-Bohm discussion, which is exactlywhat Aharonov and Casher claim in 1984 [45]. Many theoretical papers havediscussed this issue [16, 17, 36, 37]. These discussions involve imbalancedforces, field momentum and relativistic terms, all of which are present in ourabove discussion. However, none of the discussions gives an explicit and exactderivation of the delicate balance of all the momentum terms, but oftenresort to a treatment of simplified systems. For example, Aharonov and D.Rohrlich [16] discuss a flux tube with a radially moving charge, instead of acharge passing by the flux tube. While the issue of whether the charge distributionof the solenoid is perturbed has been addressed [17, 36, 46], none ofthe discussions mention the relativistic electric field imbalance.As it is possible to describe a solenoid as a collection of moving chargedparticles, the above treatment of the Feynman paradox provides hope to settlethe theoretical discussion on forces. Integration over a solenoidal currentdistribution would provide an exact derivation of momentum conservationfor the Aharonov-Bohm case.